Searching for data efficiently is a key skill in programming. While algorithms like Linear Search or Binary Search are commonly used, Interpolation Search offers an interesting alternative for searching in sorted arrays. Unlike Binary Search, which always splits the array in half, Interpolation Search estimates the position of the target based on its value relative to the first and last elements. This can make it faster when the data is uniformly distributed.
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Interpolation Search is especially useful in situations where values are spread evenly, such as searching in phone directories, ID numbers, or scores. For beginners, learning this algorithm not only introduces a clever variation of Binary Search but also strengthens understanding of array indexing, calculation of estimated positions, and efficient searching. By practicing Interpolation Search in PHP, beginners can gain practical skills for optimized data retrieval in real-world applications.
Program 1: Basic Interpolation Search Using Loops
This program demonstrates a standard Interpolation Search using a loop to find a target number in a sorted array.
<?php
$array = [10, 20, 30, 40, 50, 60, 70];
$target = 40;
$low = 0;
$high = count($array) - 1;
$found = false;
while ($low <= $high && $target >= $array[$low] && $target <= $array[$high]) {
if ($low == $high) {
if ($array[$low] == $target) {
echo "Element $target found at index $low.";
$found = true;
}
break;
}
$pos = $low + intval((($high - $low) / ($array[$high] - $array[$low])) * ($target - $array[$low]));
if ($array[$pos] == $target) {
echo "Element $target found at index $pos.";
$found = true;
break;
}
if ($array[$pos] < $target) $low = $pos + 1;
else $high = $pos - 1;
}
if (!$found) echo "Element $target not found.";
?>This program works by estimating the position of the target using a formula that considers the distribution of values. Beginners can see how the algorithm predicts where the element might be instead of checking in the middle, making it more efficient for uniformly distributed arrays.
Program 2: Interpolation Search as a Function
Wrapping Interpolation Search in a function allows reuse across multiple arrays and target values.
<?php
function interpolationSearch($arr, $target) {
$low = 0;
$high = count($arr) - 1;
while ($low <= $high && $target >= $arr[$low] && $target <= $arr[$high]) {
if ($low == $high) {
if ($arr[$low] == $target) return $low;
return -1;
}
$pos = $low + intval((($high - $low) / ($arr[$high] - $arr[$low])) * ($target - $arr[$low]));
if ($arr[$pos] == $target) return $pos;
if ($arr[$pos] < $target) $low = $pos + 1;
else $high = $pos - 1;
}
return -1;
}
$array = [5, 15, 25, 35, 45, 55];
$target = 35;
$index = interpolationSearch($array, $target);
if ($index != -1) echo "Element $target found at index $index using function.";
else echo "Element $target not found using function.";
?>Using a function improves readability and modularity. Beginners learn how to encapsulate logic and make their code reusable while practicing how Interpolation Search works in an easy-to-understand format.
Program 3: Recursive Interpolation Search
Interpolation Search can also be implemented recursively, demonstrating a divide-and-conquer approach.
<?php
function recursiveInterpolationSearch($arr, $low, $high, $target) {
if ($low <= $high && $target >= $arr[$low] && $target <= $arr[$high]) {
if ($low == $high) {
if ($arr[$low] == $target) return $low;
return -1;
}
$pos = $low + intval((($high - $low) / ($arr[$high] - $arr[$low])) * ($target - $arr[$low]));
if ($arr[$pos] == $target) return $pos;
if ($arr[$pos] < $target) return recursiveInterpolationSearch($arr, $pos + 1, $high, $target);
else return recursiveInterpolationSearch($arr, $low, $pos - 1, $target);
}
return -1;
}
$array = [2, 4, 6, 8, 10, 12];
$target = 10;
$index = recursiveInterpolationSearch($array, 0, count($array) - 1, $target);
if ($index != -1) echo "Element $target found at index $index using recursion.";
else echo "Element $target not found using recursion.";
?>The recursive approach helps beginners understand how the search space is divided and reduced in a natural, step-by-step manner. It also reinforces base cases and recursive calls, which are essential concepts in programming.
Program 4: Interpolation Search with Multiple Occurrences
This program demonstrates how to find all occurrences of a target value in a sorted array, even though Interpolation Search usually finds the first match.
<?php
$array = [5, 10, 10, 10, 15, 20];
$target = 10;
$indices = [];
$low = 0;
$high = count($array) - 1;
while ($low <= $high && $target >= $array[$low] && $target <= $array[$high]) {
if ($low == $high) {
if ($array[$low] == $target) $indices[] = $low;
break;
}
$pos = $low + intval((($high - $low) / ($array[$high] - $array[$low])) * ($target - $array[$low]));
if ($array[$pos] == $target) {
$i = $pos;
while ($i >= 0 && $array[$i] == $target) { $indices[] = $i; $i--; }
$i = $pos + 1;
while ($i < count($array) && $array[$i] == $target) { $indices[] = $i; $i++; }
break;
}
if ($array[$pos] < $target) $low = $pos + 1;
else $high = $pos - 1;
}
if (!empty($indices)) echo "Element $target found at indices: " . implode(", ", $indices) . ".";
else echo "Element $target not found.";
?>This example shows how to adapt Interpolation Search for practical needs, like finding duplicates. Beginners learn how to extend algorithms to handle real-world situations while maintaining efficiency.
Program 5: Interpolation Search Function with Error Handling
This program adds error handling to ensure the array has distinct values and prevents division by zero, making it safer for beginners to practice.
<?php
function safeInterpolationSearch($arr, $target) {
$low = 0;
$high = count($arr) - 1;
while ($low <= $high && $target >= $arr[$low] && $target <= $arr[$high]) {
if ($arr[$high] == $arr[$low]) {
if ($arr[$low] == $target) return $low;
return -1;
}
$pos = $low + intval((($high - $low) / ($arr[$high] - $arr[$low])) * ($target - $arr[$low]));
if ($arr[$pos] == $target) return $pos;
if ($arr[$pos] < $target) $low = $pos + 1;
else $high = $pos - 1;
}
return -1;
}
$array = [3, 6, 9, 12, 15];
$target = 12;
$index = safeInterpolationSearch($array, $target);
if ($index != -1) echo "Element $target found at index $index safely.";
else echo "Element $target not found safely.";
?>Adding error handling teaches beginners to write robust code. It shows the importance of checking for edge cases and preventing runtime errors while maintaining algorithm efficiency.
Frequently Asked Questions (FAQ)
Interpolation Search is an efficient algorithm but raises common questions for beginners.
Q1: When should I use Interpolation Search?
It is best for uniformly distributed and sorted arrays.
Q2: Is Interpolation Search faster than Binary Search?
It can be faster for uniform distributions but slower for uneven distributions.
Q3: Can Interpolation Search work with strings?
No, it works best with numerical data due to its formula-based estimation.
Q4: What is the time complexity of Interpolation Search?
The average complexity is O(log log n), but the worst case is O(n) for non-uniform distributions.
Q5: Can Interpolation Search handle duplicates?
Yes, with additional scanning to find all occurrences, as demonstrated in examples.
Conclusion
Interpolation Search is a clever and efficient way to search sorted arrays when the data is evenly distributed. By practicing loops, recursion, handling multiple occurrences, and adding error handling, beginners can develop a solid understanding of the algorithm and its practical applications. These PHP examples make it easy to see how Interpolation Search works step by step, preparing learners for more advanced searching and data retrieval tasks in real-world projects.
